Finite difference modeling of acoustic fields in cased holes under LWD conditions based on CFS-NPML in a cylindrical coordinate system

Key words:  complex-frequency-shifting  perfectly-matched-layer  acoustic logging-while-drilling  cementing quality evaluation  finite difference

Abstract:

In this paper, the finite-difference time-domain method with a complex-frequency-shifting nonsplitting perfectly-matched-layer (CFS-NPML) absorption boundary condition in a cylindrical coordinate system is utilized to simulate the acoustic fields in cased wells excited by monopole LWD tools. The propagation characteristics of mode waves are analyzed in the situations with different annulus positions and bond indexes. The numerical simulation results show that compared with the NPML absorption boundary condition, the CFS-NPML absorption boundary condition has better absorption effect and higher computational stability. The varieties of casing wave changing with the annulus position under LWD conditions are basically consistent with those under wireline-logging conditions. However, the influence of cased well environments on collar waves is relatively small. The casing wave velocity is similar to the collar wave velocity. Thus, these two waves overlap in time domain when the offset is small. With the increase of the bond index, the amplitude of head wave decreases rapidly at first and then remains unchanged.